{"paper":{"title":"The weighted moduli spaces of sextics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lubjana Beshaj, Scott Guest","submitted_at":"2018-03-26T18:09:51Z","abstract_excerpt":"We use the weighted moduli height as defined in \\cite{sh-h} to investigate the distribution of fine moduli points in the moduli space of genus two curves.\n  We show that for any genus two curve with equation $y^2=f(x)$, its weighted moduli height $\\mathfrak h (\\mathfrak{p}) \\leq 2^3 \\sqrt{3 \\cdot 5 \\cdot 7} \\, \\cdot H(f)$, where $H(f)$ is the minimal naive height of the curve as defined in \\cite{height}. Based on the weighted moduli height $\\mathfrak h$ we create a database of genus two curves defined over $\\mathbb Q$ with small $\\mathfrak h$ and show that for small such height ($\\mathfrak h <"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09773","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}